`C_2H_5OH and CH_3OCH_3` are

Options

A. position isomers
B. functional isomers
C. metamers
D. chain isomers

Explanation

To determine how \( C_2H_5OH \) (ethanol) and \( CH_3OCH_3 \) (dimethyl ether) are related in terms of isomerism, we will analyze their structures and functional groups.

### Step-by-Step Solution:

1. **Identify the Compounds**:
- The first compound is \( C_2H_5OH \), which is known as ethanol. It consists of a two-carbon chain with a hydroxyl group (-OH) attached to one of the carbons.
- The second compound is \( CH_3OCH_3 \), which is known as dimethyl ether. It consists of an oxygen atom bonded to two methyl groups (CH3).

2. **Determine the Molecular Formula**:
- For ethanol (\( C_2H_5OH \)):
- The molecular formula is \( C_2H_6O \) (2 carbons, 6 hydrogens, and 1 oxygen).
- For dimethyl ether (\( CH_3OCH_3 \)):
- The molecular formula is also \( C_2H_6O \) (2 carbons, 6 hydrogens, and 1 oxygen).
- Both compounds have the same molecular formula: \( C_2H_6O \).

3. **Identify the Functional Groups**:
- Ethanol contains a hydroxyl group (-OH), making it an alcohol.
- Dimethyl ether contains an ether functional group (R-O-R), where R is a carbon chain (in this case, two methyl groups).

4. **Determine the Type of Isomerism**:
- Since both compounds have the same molecular formula but different functional groups (one is an alcohol and the other is an ether), they are classified as functional isomers.
- Functional isomers are compounds that have the same molecular formula but different functional groups.

5. **Conclusion**:
- Therefore, \( C_2H_5OH \) (ethanol) and \( CH_3OCH_3 \) (dimethyl ether) are functional isomers.

### Final Answer:
**C_2H_5OH and CH_3OCH_3 are functional isomers.**

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